Chapter 5, Problem 8RAT

When you jump from an elevated position to the ground below, the force your experience when landing depends on

(a) the jumping height.

(b) the softness or hardness of the ground.

(c) how much your knees bend.

(d) All of the above.

To determine

The correct option of the statement, “When you jump from an elevated position to the ground below, the force your experience when landing depends on”.

Answer to Problem 8RAT

The correct option of the statement, “When you jump from an elevated position to the ground below, the force your experience when landing depends on”, is Option (d).

Explanation of Solution

Write the expression for the impulse.

$I=Ft$

Here,

$F$ is the force

$t$ is the time of duration

Write the relation between the change in momentum and impulse.

$\begin{array}{l}I=\Delta p\\ I=p_2-p_1\end{array}$

Here,

$p_2$ is the final momentum

$p_1$ is the final momentum

Equate both the above equations.

$p_2-p_1=Ft$

As the final momentum of the body becomes zero when the person falls on the floor, the velocity and thus the momentum becomes zero.

Substitute $0$ for $p_1$ in the above equation to get $F$.

$\begin{array}{c}Ft=0-p_1\\ F=-\frac{p_1}{t}\end{array}$

So, from the expression it can be observed that the force acting over the body is inversely proportional to the time, and negative value of force represent the retarding force.

When a person jumps from a height, a certain amount of force is experienced by the person exerted by the floor. If a person jumps from a higher point, more will be the action force exerted by the person on the ground. So, the reaction force will be exerted on the person by the ground of equal magnitude.

According to the momentum-impulse theorem, if the impact time gets reduced, then the impact force increases or vice versa. So, when a person jumps on soft ground, the time of impact increases, which results in a smaller impact force. Since the force of impact decreases, the injury caused to the person will be less.

When the person lands on the ground, more he/she bends the knee the longer will be the time of impact. As the time of impact is greater, the impact force will be smaller, resulting in less injury to the person.

Conclusion:

Therefore, the correct option of the statement, “When you jump from an elevated position to the ground below, the force your experience when landing depends on”, is option (d).